An Efficient Numerical Method for the Quintic Complex Swift-Hohenberg Equation
Hanquan Wang,Lina Yanti +1 more
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TLDR
In this paper, an efficient time-splitting Fourier spectral method for the quintic complex Swift-Hohenberg equation is presented, which is easy to apply and second-order in time and spectrally accurate in space.Abstract:
In this paper, we present an efficient time-splitting Fourier spectral method for the quintic complex Swift-Hohenberg equation. Using the Strang time-splitting tech- nique, we split the equation into linear part and nonlinear part. The linear part is solved with Fourier Pseudospectral method; the nonlinear part is solved analytically. We show that the method is easy to be applied and second-order in time and spectrally accurate in space. We apply the method to investigate soliton propagation, soliton interaction, and generation of stable moving pulses in one dimension and stable vortex solitons in two dimensions. AMS subject classifications: 65M70, 65Z05read more
Citations
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Stable Localized Solutions of Arbitrary Length for the Quintic Swift-Hohenberg Equation
TL;DR: In this paper, the authors show that localized solutions of arbitrary length are stable over a finite parameter interval of subcritical values for the quintic Swift-Hohenberg equation with a destabilizing cubic term.
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Influence of higher-order nonlinear effects on optical solitons of the complex Swift-Hohenberg model in the mode-locked fiber laser
TL;DR: In this article , the dynamics process of the traditional soliton and M−type soliton pulses in the mode-locked fiber laser is demonstrated based on the complex Swift-Hohenberg equation (CSHE) model with higher-order nonlinear effects.
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Swift-Hohenberg soliton explosions
TL;DR: In this article, new soliton explosions in the context of the complex Swift-Hohenberg equation (CSHE) have been found and analyzed in both temporal and spectral domains.
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Reliable iterative methods for 1D Swift–Hohenberg equation
TL;DR: In this article, the nonlinear problem of the 1'D Swift-Hohenberg equation (S-HE) has been solved by using five reliable iterative methods, namely, the Daftardar-Jafari method, the first one is the DJM method, and the second one is (DJM), and the third one is a variant of DJM.
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Complex Swift Hohenberg equation dissipative soliton fiber laser
TL;DR: In this paper, the authors have demonstrated a CSHE dissipative soliton fiber laser experimentally using a unique spectral filter with a complicated transmission profile, and the behavior and performance of the laser agree qualitatively with the numerical simulations based on CSHE.
References
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Journal ArticleDOI
On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
TL;DR: In this paper, a time-splitting spectral approximation for the Schrodinger equation in the semiclassical regime is proposed. But the authors consider the case where the Planck constant e is small and require the spatial mesh size h = O(e) and the time step k = o(e).
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Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg-Landau equation approach.
TL;DR: This work has found zero-velocity, moving and exploding pulsating localized structures, period doubling of pulsations and the sequence of PD bifurcations, and found chaotic pulsating solitons of the Ginzburg-Landau equation.
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Localized states in the generalized Swift-Hohenberg equation.
John Burke,Edgar Knobloch +1 more
TL;DR: The Swift-Hohenberg equation with quadratic and cubic nonlinearities exhibits a remarkable wealth of stable spatially localized states that are related to a phenomenon called homoclinic snaking.
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Swift-Hohenberg equation for lasers.
TL;DR: Pattern formation in large aspect ratio, single longitudinal mode, two-level lasers with flat end reflectors, operating near peak gain, is shown to be described by a complex Swift-Hohenberg equation coupled to a mean flow.